| aylmer.test {aylmer} | R Documentation |
A generalization of Fisher's exact test; much of the documentation and
R code is inspired by fisher.test()
aylmer.test(x, alternative = "two.sided", simulate.p.value = FALSE, n = 1e5, B = 2000, burnin = 100, use.brob = FALSE) aylmer.function(x, func, simulate.p.value = FALSE, n = 1e5, B = 2000, burnin=100, use.brob=FALSE, DNAME=NULL) prob(x, give.log=TRUE, use.brob = FALSE)
x |
A matrix, possibly with some NA entries, coerced
to integer (an object of class board) |
alternative |
Indicates the alternative hypothesis. If not a
function, it must be one of “two.sided”, “greater” or
“less”. You may specify just the initial letter. Only used
in cases with one degree of freedom. If a function, then control is
passed to aylmer.function(), for which aylmer.test()
is a wrapper |
simulate.p.value |
Boolean, with default FALSE meaning to
return the results of an exact (combinatorial) test, and TRUE
meaning to compute p-values by Monte Carlo simulation |
n |
Integer specifying the maximum number of boards to list if
simulate.p.value is FALSE; passed to allprobs()
and thence no.of.boards(). This argument has a finite
default value to prevent infinite looping |
B |
Integer specifying the number of replicates used in the Monte Carlo version of the test |
burnin |
Integer specifying the length of burn in. See details section |
use.brob |
Boolean, with default FALSE meaning to use
IEEE
arithmetic and TRUE meaning to use Brobdingnagian arithmetic |
give.log |
In function prob(), Boolean with default TRUE
meaning to return the logarithm of the answer and FALSE
meaning to return the value |
func |
In function aylmer.function(), the test function
used. The p-value returned is the probability that a random
permissible board has a test function less than that of argument
x |
DNAME |
In function aylmer.function(), the name of the
dataset to be specified; default value of NULL means to use
standard construction |
If simulate.p.value is TRUE, a vector of random
probabilities is used instead of the full enumeration. A total of
B+burnin boards are generated of which the first burnin
are discarded.
An object of class “htest”
Function prob() gives a number that is proportional to the
probability of observing a board.
The probability of observing a board B with no NAs,
conditional on its being permissible is, obvious notation,
ommitted; see pdf
The numerator is the same for any permissable board so is not calculated.
If simulate.p.value is TRUE, the default value for
B of 2000 is likely to be low, especially for large tables, or
tables with large entries. Bear in mind that the Markov chain has high
sequential correlation.
If simulate.p.value is FALSE, enumerative techniques are
used. In this case, the default value for n (10^5) is also
likely to be low: a p-value of 1 is returned because the first few
boards all have a probability much much smaller than that of the data.
Robin K. S. Hankin (R); Luke J. West (C++); an anonymous
JSS referee who suggested the approach used in
aylmer.function()
aylmer.function())
data(iqd) aylmer.test(iqd) ## Not run: aylmer.test(iqd,simulate.p.value=TRUE) data(frogs) prob(frogs) prob(frogs,use.brob=TRUE)